6(1) Example of Factor Analysis of Correlations
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Research Question
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:
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People spend time on different activities
The dataset Timbugt.Dat shows average time spent by twenty eight population
groups on 10 major activities The population groups were selected according
to the following criteria Sex, Marital Status, Employment Status and Country.
The research question is: What is the structure of relationships between
activities, between population groups, between activities and population
groups?
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Methodology
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:
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Factor Analysis of Correlations (Since the
data matrix is not a contingency table, factor analysis of correlations
was chosen as data analytic technique in preference to factor analysis
of correspondences).
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Dataset
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TIMBUGT.DAT |
SYNTAX*
$RUN FACTOR
$FILES
PRINT = TIMBUGT.LST
DICTIN = TIMBUGT.DIC
DATAIN = TIMBUGT.DAT
$SETUP
FACTOR ANALYSIS OF TIME BUDGET DATA
BADDATA=MD1 -
ANALYSIS=(NOCRSP,CORR) -
PVARS=(V2-V11) -
IDVAR=V1 -
NFACT=4 -
PRINT=(CDICT,STAT,MATR,VFPR,OFPR)
Note: All options set at default values
EXTRACT FROM COMPUTER OUTPUT
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After filtering 28 cases read from the input data file
Records kept= 28 / 28 in file; Weight of principal indiv. obs. in set
: 28.00
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Core matrix 5 P# 1 ( multiplied by 10000 ) ========
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WORK |
TRAN |
HOUS |
CHIL |
SHOP |
PERS |
MEAL |
SLEE |
TELE |
LEIS |
| WORK |
10000 |
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| TRAN |
9322 |
10000 |
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| HOUS |
-9074 |
-8691 |
10000 |
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| CHIL |
-8701 |
-8089 |
8613 |
10000 |
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| SHOP |
-6571 |
-5029 |
5010 |
5426 |
10000 |
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| PERS |
-1110 |
-791 |
-349 |
1239 |
5931 |
10000 |
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| MEAL |
-5102 |
-6492 |
3844 |
4841 |
-175 |
-1836 |
10000 |
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| SLEE |
-5433 |
-7245 |
4628 |
3203 |
112 |
-1856 |
7085 |
10000 |
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| TELE |
-565 |
-437 |
-2060 |
1216 |
2156 |
3216 |
3798 |
764 |
10000 |
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| LEIS |
-1914 |
-1053 |
-1125 |
-1086 |
2363 |
736 |
28 |
868 |
-957 |
10000 |
Trace= .10000E+02
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Eigenvalues VAL(1)= 4.6913
--------------------------------------------------------------------------------------------------------------
| NO |ITER| Eigenvalue | Percent | Cumul |*| Histogram of eigenvalues
--------------------------------------------------------------------------------------------------------------
| 1 | 0 | 4.691324 | 46.913 | 46.913 |*|***************|***************|***************|***************
| 2 | 1 | 1.874915 | 18.749 | 65.662 |*|***************|*********
| 3 | 2 | 1.374044 | 13.740 | 79.403 |*|***************|***
| 4 | 2 | 1.127411 | 11.274 | 90.677 |*|**************
-------------------------------------------------------------
| 5 | 2 | .492555 | 4.926 | 95.603 |*|******
| 6 | 2 | .258000 | 2.580 | 98.183 |*|***
| 7 | 2 | .110703 | 1.107 | 99.290 |*|*
| 8 | 2 | .043163 | .432 | 99.721 |*|*
| 9 | 5 | .026898 | .269 | 99.990 |*|
-----------------------------------------------
| 10 | 2 | .000978 | .010 | 100.000 |*|
CORRELATIONS Factors FACTOR ANALYSIS OF TIME BUDGET DATA
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Table of principal cases factors
---*----*--------------*--------------*--------------*--------------*---------------*------
| IPR | QLT WEIG INR| 1#F COS2 CPF| 2#F COS2 CPF| 3#F COS2 CPF| 4#F COS2 CPF|
---*----*--------------*--------------*--------------*--------------*----------------*-----
1| 1| 848 0 30|-1710 345 22| -843 84 14|-1829 395 87| 448 24 6|
2| 2| 793 0 25| -111 2 0|-2225 696 94| -465 30 6| 678 65 15|
3| 3| 914 0 89| 4053 661 125|-2392 230 109| -571 13 8| -507 10 8|
4| 4| 781 0 32|-1726 330 23| -425 20 3|-1890 395 93| 570 36 10|
5| 5| 830 0 68| 3379 598 87|-1465 112 41|-1512 120 59| -22 0 0|
6| 6| 900 0 32|-1433 228 16|-2067 475 81|-1117 139 32| -732 59 17|
7| 7| 786 0 45| -385 12 1|-2968 695 168| -994 78 26| 137 1 1|
8| 8| 986 0 28|-1226 192 11| 2092 560 83|-1319 223 45| -301 12 3|
9| 9| 689 0 16| 262 15 1| 1423 450 39| -445 44 5| 900 180 26|
10| 10| 982 0 73| 4205 859 135| 1342 88 34| -779 30 16| -343 6 4|
11| 11| 984 0 30|-1182 164 11| 2176 555 90|-1500 264 58| -109 1 0|
12| 12| 983 0 48| 3030 688 70| 1818 248 63| -631 30 10| 485 18 7|
13| 13| 990 0 35|-1439 214 16| 2324 559 103| -698 50 13|-1270 167 51|
14| 14| 686 0 28| 1004 130 8| 1334 230 34| -505 33 7|-1508 294 72|
15| 15| 917 0 18|-2121 895 34| 150 4 0| 25 0 0| 295 17 3|
16| 16| 985 0 25| -954 128 7| -187 5 1| 1199 203 37| 2148 650 146|
17| 17| 943 0 61| 3823 851 111| -48 0 0| 923 50 22| -852 42 23|
18| 18| 889 0 20|-2044 737 32| 244 11 1| -553 54 8| 707 88 16|
19| 19| 964 0 21| 490 41 2| 141 3 0| 1057 188 29| 2083 732 137|
20| 20| 890 0 55|-3001 582 69| -715 33 10| 1405 128 51|-1509 147 72|
21| 21| 662 0 13| -70 1 0| -723 148 10| 1129 362 33| -728 150 17|
22| 22| 948 0 19|-2111 843 34| 295 16 2| 627 74 10| -277 15 2|
23| 23| 982 0 28| -980 123 7| 254 8 1| 1403 251 51| 2169 600 149|
24| 24| 943 0 59| 3437 719 90| 507 16 5| 1789 195 83| -476 14 7|
25| 25| 949 0 19|-2205 904 37| 261 13 1| 389 28 4| -153 4 1|
26| 26| 946 0 24| 1501 336 17| 524 41 5| 1570 368 64| 1162 201 43|
27| 27| 981 0 44|-2133 369 35| -514 21 5| 1715 239 76|-2080 351 137|
28| 28| 961 0 13| -354 34 1| -314 27 2| 1574 673 64| -915 227 27|
---*-----*--------------*--------------*--------------*--------------*--------------*-------
| | 28. 0 1000| 1000| 1000| 1000| 1000|
---*-----*--------------*--------------*--------------*--------------*--------------*-------
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Table of principal variables factors
---*----*--------------*--------------*--------------*--------------*---------------
| JPR | QLT WEIG INR| 1#F COS2 CPF| 2#F COS2 CPF| 3#F COS2 CPF| 4#F COS2 CPF|
---*----*--------------*--------------*--------------*--------------*---------------
1| 2| 977 187 100| -973 946 202| 93 9 5| -133 18 13| 70 5 4|
2| 3| 966 36 100| -976 953 203| -86 7 4| -31 1 1| 67 4 4|
3| 4| 988 115 100| 893 797 170| 53 3 1| 370 137 100| 227 51 46|
4| 5| 881 14 100| 884 782 167| -106 11 6| 80 6 5| 286 82 73|
5| 6| 908 45 100| 587 344 73| -744 554 295| 76 6 4| -59 3 3|
6| 7| 779 40 100| 114 13 3| -842 708 378| -240 57 42| 17 0 0|
7| 8| 902 50 100| 644 415 88| 469 220 117| -509 259 188| -90 8 7|
8| 9| 797 327 100| 648 419 89| 510 261 139| -221 49 36| -261 68 61|
9| 10| 913 41 100| 128 16 3| -252 63 34| -909 826 601| 84 7 6|
10| 11| 956 144 100| 77 6 1| -196 38 20| 120 15 11| -947 897 796|
---*-----*--------------*--------------*--------------*--------------*--------------
| | 28.0 1000| 1000| 1000| 1000| 1000|
---*-----*--------------*--------------*--------------*--------------*--------------
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Communalities
Variable |Original final or.-fin | 1 | 2 | 3 | 4 |
--------------------------------------------------------------
1 2 | .9771 .9771 .9E-06 | -920 | 114 | 291 | 179 |
2 3 | .9657 .9657 .8E-06 | -858 | 31 | 461 | 124 |
3 4 | .9880 .9880 .1E-05 | 973 | 137 | -113 | 92 |
4 5 | .8815 .8815 .5E-06 | 884 | -161 | -206 | 176 |
5 6 | .9076 .9076 .6E-06 | 647 | -620 | 198 | -253 |
6 7 | .7790 .7790 .8E-06 | 128 | -827 | 257 | -104 |
7 8 | .9021 .9021 .8E-06 | 291 | 0 | -902 | 53 |
8 9 | .7973 .7973 .7E-06 | 372 | 210 | -767 | -158 |
9 10 | .9133 .9133 .7E-06 | -195 | -754 | -516 | 199 |
10 11 | .9562 .9562 .1E-05 | -20 | -49 | -44 | -975 |
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INTERPRETATION
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IDAMS reports that 28 cases were read from the input data file.
Weight of the principal individual observations is set equal to 28.
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Core matrix of variables:
It is the matrix of correlation coefficients. All the coefficients are
multiplied by 10,000.
Trace = Sum of the diagonal elements
=
Number of principal variables
= 10
(since there are ten variables)
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Table of Eigenvalues
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Column 1
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NO = Rank order of eigenvalues |
| Column 2 |
ITER = Number of iterations to obtain the computed value. |
| Column 3 |
Eigenvalue = l , each
eigenvalue l corresponding to the
factor a . |
| Column 4 |
Percent = Contribution of the factor to the total variance
in percentage terms. |
| Column 5 |
Cumul = percentage of variance of factor axes, considered
consecutively from the first factor axis. |
| Column 6 |
Histogram of eigenvalues = Each eigenvalue is represented by a
line of asterisks (*).
The number of asterisks is proportional to the eigenvalue.
The first eigenvalue is always represented by 60 asterisks.
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According to the criterion of average eigenvalue, only the first four
factor axes each have eigenvalue ³ 1.00
Hence, the first four factors are taken for interpretation. These factors
taken together explain more than 90% of the total variance.
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Table of Principal Cases Factors
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Column 1
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NO = Serial number of the case |
| Column 2 |
IPR = Case Idcode |
| Column 3 |
QLT = quality of representation of the point i in
the vector space, spanned by the first four factors. |
| Column 4 |
WEIG = Weight assigned to the point i. Each case is
assigned equal weight. Since the total weight of all cases = 28, the
weight of each case = 1. |
The following columns are represented for each factor
# F =
Ordinate of the case on the factor axis
COS2 = Relative contribution of the factor axis to the eccentricity
of the point i = Cosine squared of the angle formed by the vector radius
i and the factor-axis.
CPF = Relative contribution of the point
i to the variance of the factor axis.
QLT indicates that all the row points are well represented in the vector
space spanned by the first four axes.
- Factor Axis – 1
| (i) |
The values of CPF indicate that the following rows have
more than average contribution to the orientation of the factor
axis.
Rows: 3, 5, 10, 12, 17, 20, 24, 25
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| (ii) |
The values of COS2 indicate that the following row points
are well represented on this axis.
Rows: 1, 3, 4, 5, 10, 12, 15, 17, 18, 20, 22, 24, 25,
26, 27
Note that the following row points do not contribute significantly
to the orientation of the factor axis, but they are reasonably
well represented on this axis.
Rows: 1, 4, 15, 18, 22, 26, 27
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- Factor Axis – 2
| (i) |
The values of CPF indicate that the following rows have
more than average contribution to the orientation of the factor
axis.
Rows: 2, 3, 5, 6, 7, 8, 11, 12, 13
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| (ii) |
The values of COS2 indicate that the following row points
are well represented on this axis.
Rows: 2, 6, 7, 8, 9, 11, 12, 13
Note that rows 3 and 5 have more than average contribution
to the orientation of the factor axis, but they are not represented
on this axis. Similarly row 9 is well represented on this factor
but it does not contribute to its orientation.
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- Factor Axis – 3
| (i) |
The values of CPF indicate that the following rows have
more than average contribution to the orientation of the factor
axis.
Rows: 1, 4, 5, 8, 11, 23, 24, 26, 27, 28
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| (ii) |
The values of COS2 indicate that the following row points
are well represented on this axis.
Rows: 1, 4, 11, 21, 23, 24, 26, 27, 28
Note that rows 5 and 8 have more than average contribution
to the orientation of the factor axis, but they are not represented
on this axis. Similarly row 21 is well represented on this factor
but it does not contribute much to its orientation.
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- Factor Axis – 4
| (i) |
The values of CPF indicate that the following rows have
more than average contribution to the orientation of the factor
axis.
Rows: 13, 14, 16, 19, 20, 23, 27
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| (ii) |
The values of COS2 indicate that the following row points
are well represented on this axis.Rows: 14, 16, 19, 23, 27,
13
Note that rows 13 have more than average contribution
to the orientation of the factor axis, but it is not well represented
on this axis.
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Table of Principal Variables Factors
NO, QLT, INR, # F,
CPF, COS2 have clearly been defined.
- Factor Axis – 1
| (i) |
The values of CPF indicate that the following rows have
more than average contribution to the orientation of the factor
axis.
Variables: V2, V3, V4, V5
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| (ii) |
The values of COS2 indicate that the following row points
are well represented on this axis.
Variables: V2, V3, V4, V5
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- Factor Axis – 2
| (i) |
The values of CPF indicate that the following rows have
more than average contribution to the orientation of the factor
axis.
Variables: V6, V7, V8, V9
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| (ii) |
The values of COS2 indicate that the following row points
are well represented on this axis.
Variables: V6, V7, V9
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- Factor Axis – 3
| (iii) |
The values of CPF indicate that the following rows have
more than average contribution to the orientation of the factor
axis.
Variables: V8, V10
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| (iv) |
The values of COS2 indicate that the following row
points are well represented on this axis.
Variables: V8, V10
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- Factor Axis – 4
| (i) |
The values of CPF indicate that the following variable
has more than average contribution to the orientation of the factor
axis.
Variable: V11
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| (ii) |
The values of COS2 indicate that the following variable
point is well represented on this axis.
Variables: V11
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Rotated Factors
The variable factors are rotated using the varimax procedure.
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Table of communalties and Factor Loadings
Communalities
The communality shows how well a variable is predicted by the retained
factors. It is similar to the R-Squared that would be obtained if this
variable were regressed on the factors that were retained for interpretation.
Communality = Sum of squares of factor loadings
= Sum of COS squares
=
Quality of representation of the variables in the factor space
It can be easily seen that the values of communality are exactly
the same as those of QLT.
Factor loadings
Factor loadings are the correlations between the variables and factors.
They are exactly equal to COSj .
The following variables have high loadings on this factor: V2, V3, V4,
V5.
It is a bipolar factor: The poles are:
Positive: V4, V5, V6
Negative: V2, V3
The following variables have high loadings on this factor: V6, V7, V10.
It is a unipolar factor.
The following variables have high loadings on this factor: V8, V9, V10
It is a unipolar factor.
The following variables have high loadings on this factor: V6, V10
It is a unipolar factor.
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Table 1
Contribution of explicative points to the composition of the first four factor
axes
(Absolute contribution, multiplied by 1000)
| Cloud |
Explicative points with positive coordinates |
Explicative points with negative coordinates |
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Axis 1 ( l1
= 4.691324, t 1 = 46.913)
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| Activities |
V4, V5
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V2, V3
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| Population Groups |
3, 10, 12, 17, 24
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20, 23
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Axis 2 ( l2
= 1.874915, t 2 = 18.749)
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| Activities |
V8, V9
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V6, V7
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| Population Groups |
8, 11, 12, 13
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2, 3, 5, 6, 7
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Axis 3 ( l3
= 1.374044, t 3 = 13.740)
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| Activities |
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V8, V10
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| Population Groups |
20, 23, 24, 26, 27, 28
|
1, 4, 5, 8, 11
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Axis 4 ( l4
= 1.127411, t 4 = 11.274)
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| Activities |
|
V11
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| Population Groups |
15, 19, 23
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14, 20, 27, 28
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Table 2
Contribution of the explained points to the eccentricities of the first four
factorial axes
(Relative contribution, multiplied by 1000)
| Cloud |
Explicative points with positive coordinates |
Explicative points with negative coordinates |
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Axis 1 ( l1
= 4.691324, t 1 = 46.913)
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| Activities |
V4, V5, V6 |
V2, V3 |
| Population Groups |
3, 5, 10, 12, 17, 24, 26 |
15, 18, 20, 22, 24, 27 |
| |
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Axis 2 ( l2
= 1.874915, t 2 = 18.749)
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| Activities |
V9 |
V6, V7 |
| Population Groups |
8, 9, 11, 13 |
2, 3, 6, 7 |
| |
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Axis 3 ( l3
= 1.374044, t 3 = 13.740)
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| Activities |
|
V8, V10 |
| Population Groups |
21, 23, 26, 27, 28 |
1, 4, 11, 27 |
| |
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Axis 4 ( l4
= 1.127411, t 4 = 11.274)
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| Activities |
|
V11 |
| Population Groups |
16, 19, 23 |
14 |
6(2) Example of Correspondence Analysis
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Research Question
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:
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India has scientific cooperation links with
several countries. The data (COOP.DAT) shows the number of coauthorship
links with 35 most important partner countries in eleven scientific fields.
The research question is: What is the structure of multivariate relationships
between India’s significant partner countries and eleven scientific
fields of cooperation?
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Methodology
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:
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Factor Analysis of Correspondences
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Dataset
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COOP.DAT |
SYNTAX
$RUN FACTOR
$FILES
PRINT = CORRES.LST
DICTIN = COOP.DIC
DATAIN = COOP.DAT
$SETUP
TRANSNATIONAL LINKS OF INDIAN SCIENCE
BADDATA=MD1 -
ANALYSIS=(CRSP) -
PVARS=(V2-V12) -
IDVAR=1-
NFACT=4 -
PRINT=(CDICT,STAT,VFPR,OFPR)
PLOT=USER
X=1 Y=2 varp=(rincipal,suppl)
X=3 Y=4 varp=(principal,supp)
EXTRACT FROM COMPUTER OUTPUT
INTERPRETATION
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IDAMS reports that the input data comprises:
35 rows
11 columns
5 rows and 1 column variables were treated as supplementary elements.
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Summary statistics of column variables |
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Core matrix. This is a matrix of relationships between principal
variables. The elements (Cjj’) of the matrix are calculates as follows:
where Pi. = sum of principal variable
Pj.
= Sum of the principal case values
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Table of Eigenvalues
Trace = Sum of non-trivial eigenvalues
= 1.1984 is the total inertia (variance) of the data matrix.
No. of Eigenvalues = No. of active column variables – 1 = 10-1=9
There are nine factorial axes.
The first axis has the highest eigenvalue and the last axis has the lowest
eigenvalue.
NO = Serial number of eigenvalues in decreasing order
ITER = Number of iterations to obtain the factor axes,
for each factor axis.
Eigenvalue = l a
for a =2, …..10.
for a =1 l
a =1.0
(trivial eigenvalue)
First Eigenvalue = 1.000 is trival and ignored in further analysis
Percent = Ta =Ta
=100 l a
/å (l
i) = Percentage of variance of each factor axis.
Cumu = Cumulative percentage of variance of factor axes, considered
consecutively from the first factor axis.
Histogram of eigenvalues = Each eigenvalue is represented by a
line of asterisks (*). The number of asterisks is proportional to the
eigenvalue.The first non-trivial eigenvalue is always represented by 60
asterisks.
According to the criterion of average eigenvalue, only the first four
factor axes account for more than average eigenvalue (11 percent). Hence,
these factors are taken for interpretation. All these factors together
account for 83.656% of the total variance.
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Table of cases factors
IPR = Serial number associatied with I (rows)
QLT = Quality of explanation of ith row
in the factor space (1-4)
WEIG = Weight associated with ith row.
INR = Fraction of total inertia (variance) contributed by
the ith row (multiplied by 1000).
The following columns are repeated for each factor – axis.
# F = The ordinate of a case
on the factor axis (a =1, 2, 3, 4)
COS2 = Cosine squared of the angle formed by a case and the factor
axis. It is a measure of the distance between a case and the factor. It
is also equal to the relative contribution of the factor axis to the eccentricity
of the point representing a case.
CPF = Relative contribution of a case to the variance of factor
- axis.
The values of QLT indicate that rows 15, 22, 24, 27, 28, 29, 24
are poorly represented in the vector space spanned by the first four factor
axes.
| (i) |
Values of CPF indicate that the following row points have
more than average contribution to the orientation of the axis:
Rows: 1, 5, 7, 8, 9, 10, 13, 14, 21, 25
|
| (ii) |
Values of COS2 indicate that the following row points are
well represented on this axis:
Rows: 1, 5, 7, 8, 9, 10, 13, 14, 16, 17, 21, 25, 26
|
Note that rows # 16, 17, 25, 26 are well
represented on this axis, but they are not significant in terms of their
contribution to the first axis.
| (i) |
Values of CPF indicate that the following rows have more
than average contribution to the orientation of the axis:
Rows: 1, 4, 9, 25
|
| (ii) |
Values of COS2 indicate that the following row points are
well represented on the axis:
Rows: 1, 3, 9, 25
|
| (i) |
Values of CPF indicate that the following rows are significant:
Rows: 2, 4, 6, 11, 18, 19, 20 23
|
| (ii) |
Values of COS2 indicate that the following row points are
significant (COS2>.250):
Rows: 4, 6, 11, 18, 20
|
| (i) |
Values of CPF indicate that the following row points are
significant:
Rows: 2, 5, 6, 9, 10, 12, 23
|
| (ii) |
Values of COS2 indicate that the following row points are
significant (Cos2>.250):
Rows: 2, 6, 12, 23
|
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Table of Supplementary Rows
QLT: Rows 34 is not well represented in the vector space spanned
by first four axes.
INR: Supplementary rows do not contribute to the total inertia.
The inertia of supplementary rows indicate whether the rows could play
any role in the analysis if they were used as principal rows.
| (i) |
Values of COS2 indicate that the following row points are
well represented on this axis.
Rows: 2, 6, 12, 23
|
| (i) |
Values of COS2 indicate that none of the supplementary row
points are well represented on this axis.
|
| (i) |
Values of COS2 indicate that none of the supplementary row
points are well represented on this axis.
|
| (ii) |
|
| (i) |
Values of COS2 indicate that none of the supplementary row points
are well represented on this axis.
|
| (ii) |
|
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Table of Principal Variables Factors
NO, QLT, INR, # F,
CPF, COS2 have already been defined
QLT indicates that V6 is not well represent in the vector space
spanned by the first for axes
| (i) |
Values of CPF indicate that the following column points
(i.e. variables) are well represented on this axis.
Columns: 3, 5,7
|
| (ii) |
Values of COS2 indicate that the following points (i.e.
variables) are well represented on this axis (COS2>.250):
Columns: 3, 5, 7, 8
|
| (i) |
Values of CPF indicate that the following row points are
well represented on this axis.
Columns: 7, 10
|
| (ii) |
Values of COS2 indicate that the following row points
are well represented on this axis (COS2>.250):
Columns: 7, 10, 11
|
| (i) |
Values of CPF indicate that the following row points are
well represented on this axis.
Columns: 2, 4, 10
|
| (ii) |
Values of COS2 indicate that the following row points are
well represented on this axis (COS2>.250):
Columns: 2, 4
|
| (i) |
Values of CPF indicate that the following row points are
well represented on this axis.
Columns: 4, 8
|
| (ii) |
Values of COS2 indicate that the following row points are
well represented on this axis (COS2>.250):
Columns: 4, 8
|
The above results are summarized in the following tables
|
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Table 1
Contribution of explicative points to the composition of the
first four factor axes
(Absolute contribution, multiplied by 1000)
Cloud Explicative points with positive coordinates Explicative points
with negative coordinates
Axis 1 ( l1
= .079962, t 1 = 40.305)
Column Variables V5, V7 V3
Rows 1, 9, 25 5, 7, 8, 10, 13,
14, 16, 17, 21, 26
Axis 2 ( l2 = .038363,
t 2 = 19.337)
Column Variables V7 V10
Rows 9, 25 1, 4
Axis 3 ( l3 = .027867,
t 3 = 14.047)
Column Variables V2, V10 V4
Rows 4, 11, 18 2, 6, 9, 20, 23
Axis 4 ( l4 = .019775,
t 4 = 9.968)
Column Variables V8 V4
Rows 2, 10, 12 5, 6, 9, 23
Table 2
Contribution of the explained points to the eccentricities
of the first four factorial axes
(Relative contribution, multiplied by 1000)
Cloud Explained points with positive coordinates Explained points
with negative coordinates
Axis 1 ( l1 =
.079962, t 1 = 40.305)
Column Variables V5, V7, V8 V3
Rows 1, 9, 25, 31, 32 5, 7, 8, 10, 13,
14, 16, 17, 21, 26, 30, 35
Axis 2 ( l2 = .038363,
t 2 = 19.337)
Column Variables V7 V10, V11
Rows 3, 9, 25 1
Axis 3 ( l3 = .027867,
t 3 = 14.047)
Column Variables V2 V4
Rows 4, 11, 18, 23, 29 6, 20
Axis 4 ( l4 = .019775,
t 4 = 9.968)
Column Variables V8 V4
Rows 2, 12 6, 23